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Re: ? ? ? Question on Lunars
From: Frank Reed CT
Date: 2004 Oct 27, 20:29 EDT
From: Frank Reed CT
Date: 2004 Oct 27, 20:29 EDT
Bruce S wrote:
"But even if a shorter interval had been used, there would have been a problem in clearing short distances. Most, if not all, of the popular methods of clearing were what we call "approximate." That is, they calculated a set of corrections to apply to the apparent distances. The calculations were based on some not-exactly-true assumptions. A final correction took care of this. When the distance got short, this final correction got a bit wild."
The erroneous, archaic expression 'approximate' for these methods refers to a series expansion. The series expansion and the direct triangle solution are identical to any desired degree of accuracy. It is simply not true that these methods were based on 'not-exactly-true assumptions'. They had limits of applicability like any other practical calculation. It was not difficult to extend them to shorter distances, but shorter distances were avoided for other reasons, specifically the non-linear interpolation which Bruce already mentioned but also the greater requirements for accurate altitudes at those shorter distances.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
"But even if a shorter interval had been used, there would have been a problem in clearing short distances. Most, if not all, of the popular methods of clearing were what we call "approximate." That is, they calculated a set of corrections to apply to the apparent distances. The calculations were based on some not-exactly-true assumptions. A final correction took care of this. When the distance got short, this final correction got a bit wild."
The erroneous, archaic expression 'approximate' for these methods refers to a series expansion. The series expansion and the direct triangle solution are identical to any desired degree of accuracy. It is simply not true that these methods were based on 'not-exactly-true assumptions'. They had limits of applicability like any other practical calculation. It was not difficult to extend them to shorter distances, but shorter distances were avoided for other reasons, specifically the non-linear interpolation which Bruce already mentioned but also the greater requirements for accurate altitudes at those shorter distances.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
